Noise-induced enhancement of chemical reactions in nonlinear flows
Chaos 12, 417 (2002); doi:10.1063/1.1476948
Published 20 May 2002
You are not logged in to this journal. Log in
Motivated by the problem of ozone production in atmospheres of urban areas, we consider chemical reactions of the general type: A+B
2C, in idealized two-dimensional nonlinear flows that can generate Lagrangian chaos. Our aims differ from those in the existing work in that we address the role of transient chaos versus sustained chaos and, more importantly, we investigate the influence of noise. We find that noise can significantly enhance the chemical reaction in a resonancelike manner where the product of the reaction becomes maximum at some optimal noise level. We also argue that chaos may not be a necessary condition for the observed resonances. A physical theory is formulated to understand the resonant behavior. ©2002 American Institute of Physics.
2C, in idealized two-dimensional nonlinear flows that can generate Lagrangian chaos. Our aims differ from those in the existing work in that we address the role of transient chaos versus sustained chaos and, more importantly, we investigate the influence of noise. We find that noise can significantly enhance the chemical reaction in a resonancelike manner where the product of the reaction becomes maximum at some optimal noise level. We also argue that chaos may not be a necessary condition for the observed resonances. A physical theory is formulated to understand the resonant behavior. ©2002 American Institute of Physics.
| History: | Received 31 October 2001; accepted 26 February 2002; published 20 May 2002 |
| Permalink: |
http://link.aip.org/link/?CHAOEH/12/417/1 |
EDITORIALLY RELATED
KEYWORDS and PACS
- 47.70.Fw
Fluid dynamics Reactive, radiative, or nonequilibrium flows Chemically reactive flows - 47.52.+j
Fluid dynamics Chaos - 82.33.Tb
Physical chemistry and chemical physics Reactions in various media Atmospheric chemistry - 05.45.Ac
Statistical physics, thermodynamics, and nonlinear dynamical systems Nonlinear dynamics and nonlinear dynamical systems Low-dimensional chaos - 94.10.Fa
Aeronomy and magnetospheric physics Physics of the neutral atmosphere Atmospheric composition (atomic or molecular), chemical reactions and processes - YEAR: 2002
RELATED DATABASES
PUBLICATION DATA
1054-1500 (print)
1089-7682 (online)
REFERENCES (37)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- B. Sportisse and R. Djouad,
J. Comput. Phys. 164, 354 (2000) ; - J. D. Fast, J. C. Doran, W. J. Shaw, R. L. Coulter, and T. J. Martin,
J. Geophys. Res., [Atmos.] 105, 22833 (2000) ; - S. Bronnimann, W. Eugster, and H. Wanner,
Atmos. Environ. 32, 3789 (2001) ; - E. J. Hutchinson, J. S. Mindell, and R. F. Warren,
ibid. 35, 1537 (2001) . - Here we take the word “active” to mean that the number of particles advected by the flow can change, due to chemical reactions, rather than the often used meaning that the property being advected alters the advecting flow.
- F. J. Muzzio and J. M. Ottino, Phys. Rev. A 40, 7182 (1989);
- G. Metcalfe and J. M. Ottino, Phys. Rev. Lett. 72, 2875 (1994);
- I. R. Epstein,
Nature (London) 374, 321 (1995) . - S. Edouard, B. Legras, B. Lefevre, and R. Eymard,
Nature (London) 384, 444 (1996) ;
S. Edouard, B. Legras, and V. Zeitlin, - M. P. Chipperfield, E. R. Lutman, J. A. Kettleborough, J. A. Pyle, and A. E. Roche,
J. Geophys. Res. 102, 1467 (1997) . - M. G. Balluch and P. H. Haynes,
J. Geophys. Res. 102, 23487 (1997) . - Z. Toroczkai, G. Károlyi, A. Péntek, T. Tél, and C. Grebogi, Phys. Rev. Lett. 80, 500 (1998);
- Z. Neufeld, C. López, and P. H. Haynes, Phys. Rev. Lett. 82, 2606 (1999);
- D. G. H. Tan, P. H. Haynes, A. R. MacKenzie, and J. A. Pyle,
J. Geophys. Res. 103, 1585 (1998) . - A. Mariotti, C. R. Mechoso, B. Legras, and V. Daniel,
J. Atmos. Sci. 57, 402 (2000) . - G. Károlyi, A. Péntek, I. Scheuring, T. Tél, and Z. Toroczkai,
Proc. Natl. Acad. Sci. U.S.A. 97, 13661 (2000) ;
I. Scheuring, G. Károlyi, A. Péntek, T. Tél, and Z. Toroczkai, - T. Nishikawa, Z. Toroczkai, and C. Grebogi, Phys. Rev. Lett. 87, 038301 (2001).
- Stochastic resonance was first reported in R. Benzi, A. Sutera, and A. Vulpiani,
J. Phys. A 14, L453 (1981) ;
R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, - Stochastic resonance is such an extensive field that even a partial list of the literature is prohibitive here. For review of stochastic resonance, see, for example, P. Jung,
Phys. Rep. 234, 175 (1993) ;
F. Moss, D. Pierson, and D. O'Gorman, - Other representative papers include B. McNamara and K. Wiesenfeld, Phys. Rev. A 39, 4854 (1989);
- Sigeti and Horsthemke were the first to observe that noise can be utilized to improve the temporal regularity of physical signals, a phenomenon which they called noise-induced frequency. See, D. Sigeti and W. Horsthemke,
J. Stat. Phys. 54, 1217 (1989) . - G. Hu, T. Ditzinger, C. Z. Ning, and H. Haken, Phys. Rev. Lett. 71, 807 (1993).
- A. S. Pikovsky and J. Kurths, Phys. Rev. Lett. 78, 775 (1997).
- Representative papers on coherence resonance include A. Neiman, P. I. Saparin, and L. Stone, Phys. Rev. E 56, 270 (1997);
- M. R. Maxey and J. J. Riley, Phys. Fluids 26, 883 (1983).
- E. E. Michaelides,
J. Fluids Eng. 119, 233 (1997) . - A. Babiano, J. H. E. Cartwright, O. Piro, and A. Provenzale, Phys. Rev. Lett. 84, 5764 (2000).
- I. Langmuir,
Science 87, 119 (1938) . - J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, New York, 1989).
- L. Yu, C. Grebogi, and E. Ott, in Nonlinear Structure in Physical Systems (Springer-Verlag, New York, 1990), pp. 223–231.
- A. E. Gill, Atmosphere-Ocean Dynamics (Academic, New York, 1982).
- M. DeMaria and J. D. Pickle,
J. Atmos. Sci. 45, 1542 (1988) . - J. A. Zehnder and M. J. Reeder, Meteorol. Atmos. Phys. 64, 1 (1997).
- F. J. Romeiras, C. Grebogi, and E. Ott, Phys. Rev. A 41, 784 (1990).
- Y.-C. Lai, Phys. Rev. E 60, 1558 (1999).
- The quantity
T is in fact equivalent to
S, which can be seen as follows. A physical process can be described either in the time domain: f(t), or in the frequency domain by its Fourier transform F(
). When f(t) is approximately periodic, its Fourier spectrum exhibits a peak at
p=1/
T
with width 
. Since T~1/
, we have
T
+
T~1/(
p+
)
1/
p−
/
. Thus,
T~
/
and, hence,
T=
T
/
T~
p/
~
S. - C. W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin 1983).
- P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer-Verlag, Berlin, 1992).
- R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1967).
- C. Van den Broeck, J. M. R. Parrondo, R. Toral, and R. Kawai, Phys. Rev. E 55, 4084 (1997).
K. Wiesenfeld and F. Moss,
L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998); references therein.
P. Jung, U. Behn, E. Pantazelou, and F. Moss, Phys. Rev. A 46, R1709 (1992);
J. K. Douglass, L. Wilkens, E. Pantazelou, and F. Moss,
K. Wiesenfeld and F. Moss,
J. J. Collins, C. C. Chow, and T. T. Imhoff,
J. J. Collins, C. C. Chow, and T. T. Imhoff, Phys. Rev. E 52, R3321 (1995);
M. E. Inchiosa and A. R. Bulsara, ibid. 52, 327 (1995);
C. Heneghan, C. C. Chow, J. J. Collins, T. T. Imhoff, S. B. Lowen, and M. C. Teich, ibid. 54, R2228 (1996);
M. E. Inchiosa and A. R. Bulsara, ibid. 53, R2021 (1996);
A. R. Bulsara and A. Zador, ibid. 54, R2185 (1996);
M. Misono, T. Kohmoto, Y. Fukuda, and M. Kunitomo, ibid. 58, 5602 (1996);
P. C. Gailey, A. Neiman, J. J. Collins, and F. Moss,
F. Chapeau-Blondeau and X. Godivier, ibid. 55, 1478 (1997);
A. Neiman, L. Schimansky-Geier, and F. Moss, ibid. 56, R9 (1997);
M. E. Inchiosa, A. R. Bulsara, A. D. Hibbs, and B. R. Whitecotton, Phys. Rev. Lett. 80, 1381 (1998);
D. Nozaki, J. J. Collins, and Y. Yamamoto, Phys. Rev. E 60, 4637 (1999);
D. F. Russell, L. A. Wilkens and F. Moss,
I. Goychuk and P. Hänggi, Phys. Rev. E 61, 4272 (2000);
P. Hänggi, M. E. Inchiosa, D. Fogliatti, and A. R. Bulsara, ibid. 62, 6155 (2000);
P. E. Greenwood, L. M. Ward, D. F. Russell, A. Neiman, and F. Moss, Phys. Rev. Lett. 84, 4773 (2000);
M. E. Inchiosa, J. W. C. Robinson, and A. R. Bulsara, ibid. 85, 3369 (2000);
N. G. Stocks, ibid. 84, 2310 (2000);
I. Goychuk, Phys. Rev. E 64, 021909 (2001);
N. G. Stocks and R. Mannella, ibid. 64, 030902 (2001);
N. G. Stocks, ibid. 63, 041114 (2001);
N. G. Stocks,
A. Neiman, L. Schimansky-Geier, A. Cornell-Bell, and E. Moss, ibid. 83, 4896 (1999);
J. R. Pradines, G. V. Osipov, and J. J. Collins, Phys. Rev. E 60, 6407 (1999);
D. E. Postnov, S. K. Han, T. G. Yim, and O. V. Sosnovtseva, ibid. 59, R3791 (1999);
S. K. Han, T. G. Yim, D. E. Postnov, and O. V. Sosnovtseva, Phys. Rev. Lett. 83, 1771 (1999);
B. Lindner and L. Schimansky-Geier, Phys. Rev. E 60, 7270 (1999);
61, 6103 (2000);
B. Hu and C. Zhou, ibid. 61, R1001 (2000);
G. Giacomelli, M. Giudici, S. Balle, and J. R. Tredicce, Phys. Rev. Lett. 84, 3298 (2000);
Z. Liu and Y.-C. Lai, ibid. 86, 4737 (2001);
Y.-C. Lai and Z. Liu, Phys. Rev. E 64, 066202 (2001).







